Determine whether the sequence is arithmetic. If it is, determine the common difference.
--12, 10, 32, 54,...

Answer:

This is gebber gabber but yes

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

— 2-2/2-(-1) = 0/3 = 0. So the rate of change for f(x) =X2-X over the interval [-1,2] is 0.

The function is decreasing.

The domain is the set of x-values.

The range is the set of y-values.

Answer:

3/2

Step-by-step explanation:

● (-3/8) ÷(-1/4)

Flip the second fraction by putting 1 instead 4 and vice versa.

● (-3/8)* (-4/1)

-4 over 1 is -4 since dividing by 1 gives the same number.

● (-3/8)*(-4)

Eliminate the - signs in both fractions since multiplying two negative numbers by each other gives a positive number.

●( 3/8)*4

● (3*4/8)

8 is 2 times 4

● (3*4)/(4*2)

Simplify by eliminating 4 in the fraction.

● 3/2

The result is 3/2

The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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Experimental probability refers to the probability of an event occurring when an experiment was conducted. Mathematically, this can be represented as shown below

It should be noted that in order for experimental probability to be meaningful in research, the sample size must be sufficiently large. The reason why it is important to use a large number of trials when using experimental probability to predict the result is the law of large numbers.

In statistics and probability theory, the law of large numbers is a theorem that describes the result of repeating the same experiment a large number of times. The large numbers theorem states that if the same experiment or study is repeated independently a large number of times, the average of the results of the trials must be close to the expected value. The result becomes closer to the expected value as the number of trials is increased.

Hence, it is important to use a large number of trials when using experimental probability to predict results because the result becomes closer to the expected value as the number of trials is increased

Answer:

the answer is A

Step-by-step explanation:

to find the function of the ordered pairs, the first number (X) each of the pairs need to be the same, and the (y) or second numbers all need to be different.

like

for B- (1,2) (7,9) (5,8) (1,7) - for it to be a function all the first numbers would have had to be 1 or all them should have been the same first number.

for A- (3,3) (3,2) (3,1) (3,0)- its a function because the first numbers are all the same- all 3s- and the second numbers are all different.

hope this helped!

The Prove of sinMm=sinPp are:

A triangle that is known to have only one of its interior angles to be 90° is known to be a right triangle.

Note that  sinMm=sinPp is said to be a right triangle as it has its longest side to be the right triangle and it follows the Substitution property of equality and Division property of Equality.

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Answer:

Let the length be x and the width be y.

x+3=2y

2x+2y=60

So, 2y=60-2x

60-2x=x+3

60=3x+3

57=3x

x=19

If x=19, then y=11

So, the dimensions are: length 19, width 11.

Let me know if this helps!

When parallel parked along a curb, the front and rear bumpers of your vehicle must be no more than 12 inches or one foot away from other vehicles. This distance is to ensure that there is enough space for other vehicles to maneuver around your car and to prevent any accidental collisions or damage.

It is important to note that this distance may vary depending on local laws and regulations, so it is always best to check with your local authorities for specific guidelines. In addition, it is crucial to use your mirrors and signals when parallel parking to ensure that you are not blocking traffic or causing any hazards on the road. By following these guidelines and being mindful of others on the road, you can safely and effectively parallel park your vehicle.

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the answer of the question is -The current temperature and wind speed in Philadelphia

Weather describes the condition of the atmosphere, including how hot or cold, wet or dry, quiet or stormy, clear or cloudy, and so forth. The troposphere, the section of the planet's atmosphere immediately below the stratosphere, is where the majority of weather events on Earth take place.

Contrarily, climate refers to the weather patterns that can be determined by using data collected in a certain area over an extended period of time to produce adequate averages.

There are several weather conditions, such as cloudy, sunny, wet, windy, and snowy. Air masses are among the most important variables that impact the weather.

answer of the question is -The current temperature and wind speed in Philadelphia

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Answer:

\(y = \frac{1}{2}x\)

Step-by-step explanation:

First plot (3,1). Then use the slope to create the second point. Go up 1, right 2.

Next draw a line connecting the points. The line touches the y-axis at 0.

\(y = mx + b\) is the form you use.

~theLocoCoco

Answer:

0.772

Step-by-step explanation:

Original equation:

\(18 * 2^{5t}=261\)

Divide both sides by 18

\(2^{5t} = 14.5\)

Rewrite in logarithmic form (\(b^x=c \implies log_bc=x\))

\(log_214.5 = 5t\)

Divide both sides by 5

\(\frac{log_214.5}{5}=t\)

Rewrite the equation so that base is 10 using change of base formula: \(log_ba = \frac{log_na}{log_nb}\)

\(\frac{(\frac{log14.5}{log2})}{5}=y\)

Keep, change, flip

\(\frac{log14.5}{log2}*\frac{1}{5} = \frac{log14.5}{5 * log2}\)

Use a calculator to approximate log14.5 and log2

\(\frac{1.161368}{5 * 0.301029996} = t\)

Multiply in denominator

\(\frac{1.161368}{1.505149978} = t\)

Divide two values

\(t\approx 0.771596\)

Round to nearest thousandth

\(t\approx 0.772\)

A  marketing research firm was hired to conduct a study on the number of alcoholic drinks consumed by individuals in a metropolitan area over a week's time. The firm would sample adults, collect data through surveys or interviews, and analyze the data to gain insights into drinking patterns in the area.

The purpose of this study is to understand the drinking patterns of individuals in the metropolitan area. By conducting this research, the marketing research firm aims to gain insights into the average number of alcoholic drinks consumed by adults in a week's time.

The firm would start by selecting a representative sample of adults from the metropolitan area. This sample should be diverse and reflect the demographics of the population.

The firm may use random sampling methods to ensure that the sample is unbiased and representative.

Once the sample is selected, the marketing research firm would then administer a survey or conduct interviews with the participants. The survey or interviews would include questions about the number of alcoholic drinks consumed by the individuals over the course of a week. The participants may be asked to provide estimates or keep a diary of their drinking habits.

After collecting the data, the marketing research firm would analyze it to determine the average number of alcoholic drinks consumed by adults in the metropolitan area during a week. They may also look for patterns or trends in the data to understand the factors that influence drinking habits.

This study aims to provide valuable information for understanding and addressing alcohol consumption in the metropolitan area.

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The consumer's preferences are represented by the utility function \(U(x,y) = x^{0.4 }* y^{0.6}.\) We need to calculate the Marshallian demand for pants and shirts, as well as the Hicksian demand for pants and shirts.

a) To calculate the Marshallian demand for pants, we need to maximize the utility function U(x, y) subject to the consumer's budget constraint and the prices of pants and shirts. The Marshallian demand for pants (x*) can be found by taking the partial derivative of U(x, y) with respect to x and setting it equal to the ratio of the prices of pants and shirts \((P_x / P_y)\):

∂U/∂x =\(0.4 \times x^{(-0.6)} \times y^{0.6}\) = \(P_x / P_y\)

By rearranging the equation, we can solve for x* in terms of y:

\(x^* = (0.4 \times y^{0.6} \times P_x / P_y)^{(1/0.6)}\)

b) Similarly, to calculate the Marshallian demand for shirts, we take the partial derivative of U(x, y) with respect to y and set it equal to the inverse of the price ratio:

∂U/∂y =\(0.6 \times x^{0.4} \times y^{(-0.4) }= P_y / P_x\)

Solving for y*, we have:

y* =\((0.6 \times x^{0.4}\times P_y / P_x)^{(1/0.4)}\)

c) The Hicksian demand for pants (\(x_{hicks}\)) can be obtained by minimizing the expenditure function E(p, u) subject to the utility level u and the prices of pants and shirts. Since the utility function is Cobb-Douglas, the Hicksian demand for pants is the same as the Marshallian demand:

\(x_{hicks} = x^*\)

d) Similarly, the Hicksian demand for shirts \((y_{hicks})\) is also equal to the Marshallian demand for shirts:

\(y_{hicks }= y^*\)

Therefore, both the Hicksian demand and the Marshallian demand for pants and shirts are the same in this case.

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According to the empirical rule, roughly 68% of the normal distribution is within 1 standard deviation of the mean.

In this case, that tells us 68% of the population is between x = 65 and x = 79. The center is at mu = 72, which is the highest point. On either side of this center is where the curve goes downward as you move away from the center. Note the symmetry as well. Each tickmark represents 1 standard deviation unit.

Because 68% of the class got scores between x = 65 and x = 79, this means 100% - 68% = 32% of the class got a score x such that x < 65, or x > 79

Cut this in half and get (32%)/2 = 16%

16% of the population is in either tail.

16% of the population is the set of x values such that x < 65; we can say that 16% of the population is more than 1 standard deviation from the mean, and also smaller than the mean.

The 16th percentile is the marker where 16% of the population is below that value.

Therefore, the 16th percentile is the value  65  

16% of the class scored less than 65 on the test.

Considering the situation described of the sack, and that the ball was originally at the 31 yard line, the ball ends up at the 21 yard line.

We have to consider a few things.

Researching this problem on the internet, we found that originally the team had the ball at their own 31 yard line, that is, on the defense. 10 yards back from that is the 21 yard line, hence, after the sack, the ball ends up at the 21 yard line.

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Answer:

x=4

Step-by-step explanation:

16/4=4

x=4

The central angle is solved and wheel turns while the car travels 2 meters is 5.5556 radians, and while the car travels 5 meters, it is 13.8889 radians

Given data ,

To find the angle (in radians) that the wheel turns while the car travels a given distance, we can use the formula:

Angle (in radians) = Distance / Radius

a)

For a distance of 2 meters (200 cm):

Angle (in radians) = 200 cm / 36 cm

Angle (in radians) = 5.5556 radians

b)

For a distance of 5 meters:

Angle (in radians) = 500 cm / 36 cm

Angle (in radians) = 13.8889 radians

Hence , the angle (in radians) that the wheel turns while the car travels 2 meters is approximately 5.5556 radians, and while the car travels 5 meters, it is approximately 13.8889 radians

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361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;

Volume of candy bag = 528 in.³

Number of lollipop candies the bag can hold = 361 candies

Number of gummy bear candies the bag can hold = 697 candies

Therefore;

\(1 \: lollipop = \frac{528}{361} = 1.46\)

\(1 \: gummy \: bear = \frac{528}{697} = 0.76\)

Which gives the following equation;

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Answer:

l/361 + g/697= 1

Khan Academy Sat Practice

The probability of getting four of a kind in a hand of 7 cards is approximately 0.0001813.

To calculate the probability of getting four of a kind in a hand of 7 cards, we can break it down into two steps:

Step 1: Calculate the probability of getting four cards of the same value.

The first card can be any value, so the probability is 1. The second card must match the value of the first card, so the probability is 3/51 (there are 3 remaining cards of the same value out of the remaining 51 cards). The third and fourth cards must also match the same value, so the probabilities are 2/50 and 1/49, respectively.

Step 2: Calculate the probability of getting three different cards for the remaining three cards.

After getting four cards of the same value, there are 48 cards remaining. The first of the remaining three cards can be any value other than the four of a kind, so the probability is 48/48. The second card must be a different value than the first card, so the probability is 36/47. The third card must be different from the first two, so the probability is 24/46.

Multiplying the probabilities from Step 1 and Step 2 together, we get:

(1) × (3/51) × (2/50) × (1/49) × (48/48) × (36/47) × (24/46) = 0.0001813

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According to the information we can infer that the probability that the hand will contain four of a kind in the given card game is approximately 0.0015.

To calculate the probability of obtaining a four of a kind hand, we need to consider the number of ways to get a four of a kind hand divided by the total number of possible hands.

First, let's calculate the number of ways to get a four of a kind hand. We have 13 different card values (Ace, 2, 3, ..., 10, Jack, Queen, King), and for each value, we need to choose 4 cards out of the 4 available in the deck. So, there are 13 ways to choose the four cards of the same value.

Next, we need to calculate the number of ways to choose the remaining 3 cards with different values. We have 12 remaining card values (excluding the one used for the four of a kind), and for each value, we need to choose 1 card out of the 4 available. Therefore, there are 12 * 4 * 4 = 192 ways to choose the remaining 3 cards.

Now, let's calculate the total number of possible hands. In this card game, each player starts with a hand of 2 cards and then draws 5 more, so the total number of possible hands is given by the combination of 7 cards taken from a deck of 52 cards, which is denoted as C(52, 7) = 133,784,560.

Finally, we can calculate the probability by dividing the number of ways to get a four of a kind hand by the total number of possible hands:

So, we can conclude that the probability of obtaining a four of a kind hand in the given card game is approximately 0.0015, rounded to four decimal places.

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Answer:

Explanation:

solve:

1.

y = 44 - 5 - 3x

y = 39 - 3x

2.

y = 39 - 3x

y = 39 - 3(5)

y = 39 - 15

y = 24

3.

y = 39 - 3x

0 = 39 - 3x

-39 = -3x

x = 13

He can total ride 13 rides before he runs out of money.

Answer:

B

Step-by-step explanation:

To find the y- intercept let x = 0

From the table for f(x)

When x = 0 → f(x) = - 4

That is the y- intercept = - 4

Given

g(x) = 3 \((2)^{x}\)

let x = 0 , then

g(0) = 3 \((2)^{0}\) [ \(2^{0}\) = 1 ]

       = 3 × 1

       = 3

That is the y- intercept = 3

Thus the y- intercept of g(x) is greater → B

The equation of the trend line in the graph can be found to be y = 5 x + 15

The equation of the trend line takes the form :

y = Slope ( x ) + y intercept

From the diagram, we know the y - intercept is 15 as this is where the line intercepts the y - axis.

The slope can be found by picking a point and using the formula. We will pick ( 1, 20 ).

The slope is:

20 = Slope ( 1 ) + 15

Slope = 20 - 15

Slope = 5

The equation is:

y = 5 x + 15

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According to the quadratic equation the solution of k is 48 ± 8√26.

In math the term called quadratic equation is known as the polynomial equation whose highest degree is two

As we all know that the value of the quadratic equation is written as,

=> (k - 4)x² - 3kx - 4(k -2) = 0.

Now we have identified that the given equation is in the form of ax² + bx + c = 0.

Here we have also identified the value of a = k - 4, b = -3k and c = 4(k-2)

And then we have to use the quadratic formula to identify the value of k,

Here it can be written as.

=> (-3k)² - (4 x (k - 4) x 4(k-2))

When we expand the term then we get,

=> 9k² - (16k² - 32k - 64k + 128)

When we simplify this one then  we get

=> -5k² + 96k - 128 = 0

Here we have to factorize the expression then we get the value of k as 48 ± 8√26.

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Answer:

9.9 meters

Step-by-step explanation:

7.5+2.4=9.9 meters

=========================================================

Explanation:

As you probably can guess (or already know), the term "slope intercept form" means that all we need are the slope and y intercept to get the equation.

To get the slope, we need two points. Pick any two points you want. I'll pick (3,-7) and (6,-9). Notice how we go down 2 units and then over to the right 3 units when we move from the first point to the second point.

See diagram below.

So the slope is rise/run = -2/3. The negative rise indicates we go down. The run is always moving to the right. This produces the downhill trend when we move from left to right.

--------------------

We can also use the slope formula. I'll use those two points mentioned earlier.

m = (y2-y1)/(x2-x1)

m = (-9-(-7))/(6-3)

m = (-9+7)/(6-3)

m = -2/3

We get the same result as earlier

--------------------

The y intercept is where the graph crosses the vertical y axis. This is at 5. So b = 5 is the y intercept.

Since the slope is m = -2/3 and the y intercept is b = 5, we go from y = mx+b to y = (-2/3)x-5 which is our final answer.

The roots of h(x)=x³−2x²+9x−18 is 2, -3i and 3i.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

Given:

h(x)=x³−2x²+9x−18

so, (x-2) is the solution of h(x).

Now, the synthetic division

                                  (x-2) | x³−2x²+9x−18 | x² + 9

                                            x³ −2x²

                                      __________

                                                0   + 9x - 18

                                                         9x - 18

                                                     __________

                                                               0

now, again factorize x² + 9 = 0

 x = ±3i

Hence, the roots are 2, -3i and 3i.

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